I would assert that the only difference between the NAZI ideology and communism and what we sometimes have seen across the globe is one of degrees.
Those who think that they know better how others should live are NAZIs. Be they the Taliban, the communists under Mao, under Stalin, or any of a thousand different ideologies. The basic premise remains always the same…I know better than you how to think, conform or die.
Sorry. Making up new definitions for words is always risky, but making up definitions that are more confusing than explanatory is pointless.
By your definition, Domitian, Torquemada, and Cromwell were “NAZI”'s even though they died hundreds of years before anything related to National Socialism had been envisioned by humans. Similarly, you appear to be using a definition of communism that I suspect you believe everyone will accept, even though I doubt that your definition matches that of many other people.
As noted, we already have the word authoritarianism that meets most of your points, while your description of Naziism fails to take into consideration the various aspects of fascism that separate it from communism or other authoritarian regimes.
I am not sure why you are proposing this discussion, but I suspect that you need to a bit more reading on the topics involved.
The key difference was the the Nazis (and other fascist groups) were exclusive. It wasn’t a choice of “conform or die” - many people were simply unacceptable to the Nazi ideology and wouldn’t have been allowed to join even if they had wanted to.
At least with the communists, conforming was a theoretical option. Communist ideology said anyone could become a communist. The same is true with most extremist religious groups - you can knuckle under to their tyranny and convert.
What you are describing is authortarianism statism that has no respect for human rights. There are forms of statism that are not authoritarian and that do respect human rights (western europe for example).
No, they could have applied to join - they didn’t want to. But in theory, they could have renounced their evil capitalist ways and become good communists. Heck, the Chinese communists even claimed they had reformed Puyi.
Now compare that the the Nazis. It didn’t matter how enthusiastically a hypothetical Jew might have embraced their ideology. As far as the Nazis were concerned a Jew would always remain a Jew.
Seeing as the actual acronym was NSDAP, I’d say no. I was under the impression “Nazis” comes because they would always be referring to themselves and their policy and their philosophies and just about everything they could come up with as “Nazional-Sozialistische [whatever]”, with the particular German way of pronouncing it “nATzional…etc.” so it was a quick shorthand for ‘The guys who are always talking about “nazi…etc” this and “nazi…etc.” that’.
Back to the OP:
Well, yeah, sure, what the OP seems to be doing is grabbing on to the colloquial hyperbolic usage by which we refer to “Homeowner’s Association Nazis” or “Grammar Nazis” or the “Soup Nazi” to refer to people who are compulsive prescriptivist fault-finders and bullies, and saying it applies across the board. But we actually need to be able to use it seriously in the political environment from where the term was borrowed. Are we to not make any distinction between types and forms of totalitarianism?